Torque and Angular AccelerationTorque and Angular Acceleration

AP Physics CMrs. Coyle

http://mdmetric.com/tech/torqueB.gif

Torque, Torque, • The tendency of a force to rotate an

object about an axis.• Vector quantity that is the cross product

of the lever(moment arm) and the force.

r┴ x F = rFsin

• r is the perpendicular distance between the axis of rotation and the force.

Sign of TorqueSign of Torque

• If the rotation caused by the torque is tending to be counterclockwise the torque is positive.

• If the rotation caused by the torque is tending to be clockwise the torque is negative.

• The direction of torque is found by the right hand rule.

• The fingers wrap in the direction of the

force.

• The thumb represents the torque vector.

Direction of TorqueDirection of Torque

Units of TorqueUnits of Torque• Unit: m·N

• Note: the units are the same as that of energy, but are not equivalent, they are not a Joule.

Equilibrium:Equilibrium:• Translational F=0 Rest or Const v • Rotational =0 No rotation or

const • Mechanical Equilibrium

–Both of the above

• Static Equilibrium – Static Translational and Static Rotational–No Translation, no rotation

Example: Wheel

Two forces are acting on a wheel as shown.a) Find the torques produced by each.b) In which direction will the wheel turn?c) Is there rotational equilibrium?

r= 0.3m

Torque and Angular AccelerationTorque and Angular AccelerationTangential force

Ft = mat

Torqueτ=Ft r = mat rτ= mα r r = m r2 α

τ= I α

Torque and Angular AccelerationTorque and Angular Acceleration• For an

elemental particle dm

2 2r dm r dm

Note

is analogous to F=ma

Ex: Wheel

Ex: Two Pulleys

Ex: Two Pulleys cont’d

Note: N and mg do not supply a torque because they act through the center of rotation.

Ex: #34

• A grinding wheel is in the form of a uniform solid disk of radius 7.00cm and mass 2.00kg. It starts from rest and accelerates uniformly under the action of the constant torque of 0.600Nm that the motor exerts on the wheel.

a)How long does the wheel take to reach its final operating speed of 1200rev/min?

b)Through how many revolutions does it turn while accelerating?Ans: a) 1.03s, b) 10.3 rev

Ex: #38

• A potter’s wheel-a thick stone disk of radius 0.500m and mass 100kg- is freely rotating at 50 rev/min. The potter can stop the wheel in 6.00s by pressing a wet rag against the rim and exerting a radially inward force of 70.0N . Find the effective coefficient of kinetic friction between the wheel and rag.

• Ans: 0.312